A new spinfoam vertex for quantum gravity - General Relativity and Quantum Cosmology

Abstract: We introduce a new spinfoam vertex to be used in models of 4d quantum gravitybased on SU(2) and SO(4) BF theory plus constraints. It can be seen as theconventional vertex of SU(2) BF theory, the 15j symbol, in a particular basisconstructed using SU(2) coherent states. This basis makes the geometricinterpretation of the variables transparent: they are the vectors normal to thetriangles within each tetrahedron. We study the condition under which thesestates can be considered semiclassical, and we show that the semiclassical onesdominate the evaluation of quantum correlations. Finally, we describe how theconstraints reducing BF to gravity can be directly written in terms of the newvariables, and how the semiclassicality of the states might improveunderstanding the correct way to implement the constraints.